A diesel engine in which an engine exhaust passage is branched to a pair of exhaust branch passages for purifying NO.sub.x, a switching valve is disposed at the branched portion of these exhaust branch passages to alternately guide the exhaust gas to one of the exhaust branch passages by a switching function of the switching valve, and a catalyst which can oxidize and absorb the NO.sub.x is disposed in each of the exhaust branch passages is well known (refer to Japanese Unexamined Patent Publication No. 62-106826). In this diesel engine, NO.sub.x in the exhaust gas introduced into one exhaust branch passage is oxidized and absorbed by the catalyst disposed in that exhaust branch passage. During this time, the inflow of the exhaust gas to the other exhaust branch passage is stopped and, at the same time, a gaseous reducing agent is fed into this exhaust branch passage. The NO.sub.x accumulated in the catalyst disposed in this exhaust branch passage is reduced by this reducing agent. Subsequently, after a short time, the introduction of the exhaust gas to the exhaust branch passage to which the exhaust gas had been introduced heretofore is stopped by the switching function of the switching valve, and the introduction of the exhaust gas to the exhaust branch passage to which the introduction of the exhaust gas had been stopped heretofore is started again.
However, when the temperature of the catalyst becomes low, the oxidation and absorption of NO.sub.x can no longer be carried out. Therefore, in this diesel engine, when the temperature of the exhaust gas becomes low and therefore the temperature of the catalyst is low, the NO.sub.x is not oxidized and absorbed and therefore there is the problem that NO.sub.x is discharged to the atmosphere.